Imaging channeled spectrograph

ABSTRACT

An Imaging Channeled Spectrograph is provided which comprises a Fabry-Perot bandpass filter followed by a wide-slit imaging grating spectrograph, and which thus combines the two dimensional monochromatic imaging of a Fabry-Perot bandpass filter system with the high resolution and comprehensive wavelength coverage of a grating spectrograph. The Imaging Channeled Spectrograph produces a series of simultaneous, high resolution, non-overlapping, two dimensional monochromatic images of the entrance slit uniformly distributed over a large spectral range.

FIELD OF THE INVENTION

The present invention relates to spectroscopy and in particular to an improved spectrograph which combines a Fabry-Perot bandpass filter with a wide-slit imaging spectrograph.

BACKGROUND OF THE INVENTION

Many different instrumental techniques are commonly used to accomplish spectroscopic analysis. Hitherto, two-dimensional monochromatic images have been obtained mainly by thin-film filter systems, narrow-bandpass tunable interferometric monochromators, and wide-slit spectrographs.

Thin-film filter systems and monochromators usually require narrow bandpass thin film filters as prefilters. Since these prefilters are tunable over only a very limited spectral range, these systems do not permit simultaneous observations of multiple emission lines spread over a large spectral range.

The wide-slit spectrographs produce multiple emission line images across a broad spectral range. However, the wide-slit which permits two dimensional imaging also results in a corresponding degradation in spectral and spatial resolution. This spectrograph also suffers from image overlap when it is used to image closely packed emission lines.

SUMMARY OF THE INVENTION

In accordance with the invention an imaging channeled spectrograph is provided which includes a Fabry-Perot bandpass filter for bandpass filtering a received collimated beam of light into a filtered beam comprising a number of limited frequency bands of the light of the collimated beam, and an imaging spectrograph for receiving the filtered beam from the Fabry-Perot filter and dispersing the spectrum of the filtered beam across the focal plane of the spectrograph. The invention produces a number of two dimensional monochromatic images of the entrance slit spanning a large spectral range without image overlap and without loss of spectral or spatial resolution

In a preferred embodiment, the invention includes an entrance slit for initially receiving light from a source to be analyzed and an off-axis collimator for receiving light from the entrance slit and reflecting a collimated beam of light to the Fabry-Perot filter. A flat plane grating directs the light passed by the Fabry-Perot filter to a spherical grating. The flat plane grating and spherical grating are in a tandem Wadsworth geometry Alternatively, a plurality of Fabry-Perot filters can be used to sequentially filter the collimated beam.

Other features and advantages of the invention will be set forth in, or be readily apparent from, the detailed description of the preferred embodiment and the following drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic side view of a spectrograph in accordance with the present invention.

FIGS. 2(a) through 2(c) show a schematic representation of the spectral decomposition achieved by the embodiment of FIG. 1.

FIG. 3(a) through 3(c) show a schematic representation of the spectral decomposition achieved by an alternative embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to FIG. 1 which shows a preferred embodiment of an Imaging Channeled Spectrograph according to the present invention. The Imaging Channeled Spectrograph 10 includes an entrance slit 12 having an adjustable width; an off-axis collimator 14; a tunable, bandpass Fabry-Perot filter 16; a spectrographic flat grating 18; and a spectrographic spherical grating 20. These components are arranged such that light to be analyzed passes through entrance slit 12 and is collimated and reflected by off-axis collimator 14. The collimated beam of light is then filtered by Fabry-Perot filter 16 to provide a beam with multiple, narrow, spectral bandwidth "spikes". The filtered collimated beam is then diffracted by flat grating 18 onto spherical grating 20. Spherical grating 20 focuses the spectrum onto the fully stigmatic focal plane 22. Photographic film (not shown) may be positioned at focal plane 22 for recording photographic images of the spectrum. Entrance slit 12, off-axis collimator 14, flat grating 18, and spherical grating 20 together comprise a wide-slit imaging grating spectrograph. Alternatively, off-axis collimator 14 could be replaced by a lens or a cassegraine telescope.

FIG. 2 shows the spectral decomposition achieved by the Imaging Channeled Spectrograph embodiment shown in FIG. 1; wherein 2(a) represents the spectral profile A of an observed sample; 2(b) represents the plural, frequency spikes B that can be passed by Fabry-Perot filter 16; and 2(c) represents the final two-dimensional, mono-chromatic images C produced at focal plane 22. Each image C corresponds to one frequency spike B passed by Fabry-Perot filter 16. As shown in FIG. 2, the narrow band output spikes B of the Fabry-Perot filter have substantially identical frequency widths and are separated by substantially equal frequency spacings.

The central wavelengths and spectral bandwidth of each image C corresponds to spike B of Fabry-Perot filter 16 at that particular central wavelength. The channel central wavelengths, that is the position of spikes B, can be tuned by adjusting the transmission profile of Fabry-Perot filter 16. Each frequency spike B has a finite spectral bandwidth. Ideally, each point within entrance slit 12 would be represented by a single point in image C. However, because of the frequency bandwidth of spike B, the single, ideal point is dispersed (blurred) along focal plane 22. This blur--due to the spectrograph dispersion of the spike bandwidth--results in a lateral chromatic aberration which degrades the spatial resolution of each channel. If the spike bandwidth is selected to be narrow, the blur is minimal.

The channel bandwidth and central wavelength are determined by the bandwidth and peak wavelength of the multiple transmission spikes B of Fabry-Perot filter 16. The location of each channel on focal plane 22, the total field of view, the spatial resolution, and the final magnification are determined by the dispersion and imaging characteristics of the wide-slit imaging grating spectrograph. The following eight principles summarize the relationship between the optional characteristics of Imaging Channeled Spectrograph 10 and the operational parameters of Fabry-Perot filter 16 and the wide-slit imaging grating spectrograph.

1) The spectral bandwidth of each channel is determined solely by the bandwidth of Fabry-Perot filter 16.

2) The spectral separation between channels is equal to the spectral separation of the bandpasses (this separation is termed the free spectral range (FSR)) of Fabry-Perot filter 16.

3) The linear separation between channels is equal to the product of the FSR and the spectrograph dispersion.

4) The linear width and height of the channels at focal plane 22 is equal to the width and height of entrance slit 12, multiplied by the magnification of the wide-slit imaging grating spectrograph.

5) The spectrograph's dispersion of the Fabry-Perot filter's finite bandwidth causes a lateral chromatic aberration at focal plane 22. The magnitude of the aberration is equal to the product of the bandwidth of Fabry-Perot filter 16 and the wide-slit imaging grating spectrograph dispersion.

6) The spatial resolution of imaging channeled spectrograph 10 is identical to the spatial resolution of the wide-slit imaging grating spectrograph with the exception of the chromatic aberration.

7) Rejection of out-of-band wavelengths determines the contrast of Fabry-Perot filter 16. Contrast is measured by the ratio of the transmission of the spikes to the transmission of the rejected frequencies: T_(max) /T_(min)

8) The spectral range is limited by the stopband width of the reflective coating on Fabry-Perot filter 16 and the usable range of the grating spectrograph.

The operational parameters of the imaging channeled spectrograph are calculated using the above eight principles combined with the optical characteristics of Fabry-Perot filter 16 and the wide-slit imaging qrating spectrograph. Table I below shows the operational parameters of Fabry-Perot filter 16, calculated for normal incidence and a cavity index of refraction equal to one, when phase terms and angular effects are neglected.

                  TABLE I                                                          ______________________________________                                         FABRY-PEROT OPERATIONAL CHARACTERISTICS                                        Characteristic      Expression                                                 ______________________________________                                         Peak wavelength of the mth order                                                                   λ.sub.m = 2d/m                                      Free spectral range - spectral                                                                     FSR = λ.sub.m.sup.2 /2d                             separation between the m and                                                   m-1, m+1 peak wavelengths                                                      Full width at half maximum of                                                                      FWHM.sub.m = FSR.sub.m /F =                                the mth wavelength spike                                                                           λ.sub.m.sup.2 /2dF                                  Finesse fixed by the                                                                               F                                                          particular Fabry-Perot cavity                                                  Cavity spacing      d                                                          Order of interference                                                                              m                                                          Inter-order contrast                                                                               C = 1/(1 + 4F.sup.2 /π.sup.2)                           Spectral range      λ.sub.iF -λ.sub.fF                           ______________________________________                                    

The Fabry-Perot bandpass filter Airy transmission profile consists of consecutive transmission spikes. The condition for constructive interference (with normal incidence and a unity index of refraction) is 2d=mλ where d is the cavity spacing and m is the interference order (m=1, 2, 3 . . . ). Thus, a particular peak wavelength λ_(m) can be specifically identified by order and cavity spacing (λ_(m) =2d/m).

The spectral separation between the λ_(m), λ_(m-1), and λ_(m+1) peak wavelengths is generally denoted as the free spectral range (FSR). The FSR is determined by the cavity spacing "d" and the particular λ_(m) : FSR_(m) =λ_(m) ² /2d; where λ_(iF) represents the wavelength at the short wavelength end of the spectral range and λ_(fF) represents the wavelength at the long wavelength end of the spectral range.

The shape of the Airy transmission profile from Fabry-Perot filter 16 can be described by its finesse F. F is a fixed property of a Fabry-Perot filter cavity: F=FSR_(m) /FWHM_(m) ; where FWHM_(m) is the full-width-at-half-maximum of the m^(th) channel. The placement of the Fabry-Perot filter into the wide-slit imaging grating spectrograph must be done with care to avoid significant degradation of the system's spectral properties. Placement of a Fabry-Perot filter into an optical system, and other important factors affecting Fabry-Perot filter performance, are discussed elsewhere (for example, see G. Hernandez, Fabry-Perot Interferometers. (Cambridge University Press, New York 1986)).

The basic parameters of a general imaging spectrograph are shown in Table II. Numerous possible configurations are described in other references (for example, M. C. Hutley, Diffraction Gratinos, (Academic Press, New York, 1982)). In Table II, lower case "s" denotes the distance along focal plane 22 and upper case "S" (in λ_(iS), λ_(fS)) denotes the short and long wavelength ends, respectfully, of the spectral range of the spectrograph.

                  TABLE II                                                         ______________________________________                                         IMAGING SPECTROGRAPH OPERATIONAL                                               CHARACTERISTICS                                                                Characteristic          Expression                                             ______________________________________                                         Linear dispersion       ds/dλ                                           Magnification           M                                                      Spectral range          λ.sub.iS -λ.sub.fS                       Spatial resolution      R                                                      (linear units at the focal plane)                                              Entrance slit width     W.sub.S                                                Entrance slit height    H.sub.S                                                ______________________________________                                    

The characteristics of the imaging channeled spectrograph of FIG. 1 are shown in Table III. The characteristics are a function of the bandpass Fabry-Perot filter and wide-slit imaging grating spectrograph operating parameters and follow the eight basic principles of operation listed above.

                  TABLE III                                                        ______________________________________                                         IMAGING CHANNELED SPECTROGRAPH                                                 OPERATIONAL CHARACTERISTICS                                                    Characteristic        Expression                                               ______________________________________                                         mth channel central wavelength                                                                       λ.sub.m = 2d/m                                    mth channel spectral resolution (FWHM)                                                               FWHM.sub.m = λ.sub.m.sup.2 /2dF                   Spectral separation between the mth                                                                  FSR.sub.m = λ.sub.m.sup.2 /2d                     channel and the m - 1, m + 1 channels                                          Linear separation between the mth                                                                    D.sub.m = FSR.sub.m × ds/dλ                 channel and the m - 1, m + 1 channels                                          at the focal plane                                                             Linear channel width  W.sub.c = W.sub.S × M < D.sub.m                    Linear channel height H.sub.c = H.sub.S × M                              Lateral chromatic aberration                                                                         A.sub.m = FWHM.sub.m ×                             in the dispersion direction                                                                          ds/dλ                                             Spatial resolution along the                                                                         limited by A.sub.m and R                                 dispersion direction                                                           Spatial resolution perpendicular                                                                     R                                                        to the dispersion direction                                                    (linear units at the focal plane)                                              The shortest detectable wavelength                                                                   λ.sub.ic is the longest of                                              λ.sub.iF and λ.sub.iS                      The longest detectable wavelength                                                                    λ.sub.fc is the shortest of                                              .sub.fF and λ.sub.fS                             Spectral range        λ.sub.ic -λ.sub.fc                         Interference order of λ.sub.ic                                                                m.sub.i = 2d/λ.sub.ic                             Interference order of λ.sub.fc                                                                m.sub.f = 2d/λ.sub.fc                             Total number of channels                                                                             m.sub.t = m.sub.i -m.sub.f =                                                   2d(1/λ.sub.ic -1/λ.sub.fc)                 Out of band rejection C = 1/(1+4F.sup.2 /π.sup.2)                           ______________________________________                                    

Images C will not overlap if W_(c) <D_(m) for all interference orders of interest. If the channels on either side of the channels of interest are blank, image overlap is not a problem and W_(c) may be increased without penalty. Alternately, if the source has a small angular extent and no significant background radiation is present, a "slitless" spectrograph could be used. The Imaging Channeled Spectrograph of this invention is a versatile and flexible instrument. The channel spectral bandwidth can be varied from broad (for applications such as obtaining emission line images or continuum measurements) to narrow (for applications requiring high spectral resolution measurements of line/continuum profiles). The width of the field of view can be adjusted to match the needs of a particular application. The height is determined by spectrograph/detector limitations: a greater height generally results in poorer image quality and increases the size of the detector required. The performance of the spectrograph elements limits the high spatial resolution that can be achieved. In practice, defects in the Fabry-Perot filter 16 place certain limitations on the performance of the system. An ideal Fabry-Perot filter could have an infinite finesse. However, the actual performance of Fabry-Perot filter 16 is degraded by relative figure errors between the two mirrors comprising the Fabry-Perot filter 16 (the two mirrors are not perfectly flat) and by absorption/scatter in the interferometer. These two defects limit finesse of Fabry-Perot filter 16 to a maximum value, F_(max), which varies widely with wavelength. For reasonable apertures, F_(max) is 100 at visible wavelengths; at UV wavelenqths (about 2288Å), it is about 35. This upper limit on the finesse necessitates certain instrumental compromises between the width of the field of view, the spatial resolution, and the spectral bandwidth.

To illustrate these compromises, the operational parameters will be discussed for three configurations of Imaging Channeled Spectrograph. Each configuration optimizes a different optical characteristic: field of view, imaging properties, and spectral resolution. For all three configurations, the selected characteristic is optimized by varying the operating parameters of Fabry-Perot filter 16 while holding the characteristics of the grating spectrograph system fixed.

The first configuration optimizes the imaging performance of the Imaging Channeled Spectrograph. This is accomplished by maximizing the width of the field of view while maintaining an adequate spatial resolution across it. From Table III, W_(c) <D_(m) =F×A_(m). Larger W_(c) can be obtained by increasing F and A_(m). A_(m),max is chosen as the maximum tolerable chromatic aberration. F can rise to F_(max). Thus,

    W.sub.c,max <D.sub.m,max =F.sub.max ×A.sub.m,max.

The fundamental limit on width of the field is the product of F_(max) and the maximum acceptable chromatic aberration.

In the second configuration, the spectral bandwidth is minimized. The bandwidth is inversely proportional to finesse and cavity spacing. Thus, F is increased to F_(max) and the cavity spacing is increased. Larger cavity spacing results in a decreased free spectral range and a corresponding decrease in the linear separation between channels at the focal plane. The linear spacing between channels must be sufficient to distinguish different channels at the Imaging Channeled Spectrograph focal plane or D_(m) >R. In this limiting case D_(m) =R is chosen. Using Table III, the following expression is derived.

    FWHM.sub.m,min =(1/F.sub.max)×(R×dλ/ds).

The last configuration maximizes the width of the field of view for a chosen spectral bandwidth (FWHM_(m)). From Table III, the expression for an upper limit of W_(c) is derived.

    W.sub.c <D.sub.m =FWHM.sub.m ×F×ds/dλ.

Thus, W_(c) for a particular FWHM_(m) is limited by FWHM_(m) ×F_(max) xds/dλ. The chromatic aberration in this configuration is equal to FWH_(m) ×ds/dλ.

In an alternative embodiment (not shown), Fabry-Perot filter 16 can be replaced by several Fabry-Perot filters in series. FIG. 3 shows the spectral decomposition achieved by an Imaging Channeled Spectrograph having two Fabry-Perot filters in series, wherein 3(a) represents the spectral profile of the observed sample; 3(b) represents the frequencies that can be passed by the first Fabry-Perot filter; 3(b') represents the frequencies that can be passed by the second Fabry-Perot filter; and 3(c) represents the final images produced at the focal plane 22. Final images are produced only for frequencies passed by both Fabry-Perot filters. As shown in FIG. 3, the series of Fabry-Perot filters pass only those frequencies passed by both individual Fabry-Perot filters. While the passed frequencies are transmitted at near 100%, the out of band frequencies are attenuated approximately twice, once in each Fabry-Perot filter. This double attenuation raises the net contrast. Thus combining the Fabry-Perot filters generally increases the spectral spacing between transmission spikes, allows a more flexible spectral resolution and enhances the inter-order contrast (See G. Hernandez, Fabry-Perot Interferometers, (Cambridge University Press, New York 1986)). The imaging channeled spectrograph using multiple Fabry-Perot filters typically has a greater field of view (since a wider entrance slit can be used), a higher out of band rejection, a more flexible spectral resolution, a larger frequency separation between images, and a larger spectral range.

In the preferred embodiment, the wide-slit imaging grating spectrograph comprises a fully stigmatic tandem Wadsworth spectrograph (fstW). In a tandem Wadsworth configuration, a flat plate grating is located on an arc passing through the concave spherical surface of a spherical grating. The device in FIG. 1 is an example of the tandem Wadsworth configuration with flat plate grating 18 and spherical grating 20. This configuration is more fully disclosed in articles such as: J.-D. F. Bartoe and G. E. Brueckner, "New Stigmatic, Coma-free, Concave Grating Spectrograph", JOSA, 65, 13, (1975). The Fabry-Perot filter comprises a tunable UV Fabry-Perot filter (as disclosed in, e.g., D. G. Socker and C. M. Korendyke, "Imaging and Spectral Performance of Fabry-Perot Interferometers at 2288Å", 168th AAS meeting, (1986).) Those skilled in the art will appreciate that there are numerous techniques for implementing a tunable Fabry-Perot filter. For instance, a reference is made to U.S. Pat. Nos. 4,400,058 (Durand et al); 4,553,816 (Durand et al); and 4,377,324 (Durand et al) and 3,612,655 (Lincoln et al.).

The characteristics of the fstW are given in Table IV. The fstW tandem Wadsworth configuration satisfies the Wadsworth mount condition for stigmatic imaging over its entire wavelength range. The net spot diagram diameter from the remaining aberrations is less than 10 μm. Furthermore, the fstW has a moderate amount of dispersion at the focal plane, provides a nearly perfect location to place the Fabry-Perot filter (in a collimated beam, close to an image of the system entrance aperture) and allows the appropriate amount of magnification to obtain the correct final plate scale.

                  TABLE IV                                                         ______________________________________                                         FULLY STIGMATIC TANDEM WADSWORTH                                               SPECTROGRAPH CHARACTERISTICS                                                   Characteristic     Expression/Value                                            ______________________________________                                         Off-axis parabolic collimator                                                                     focal length = 16.9 cm                                      Flat grating       13000 lines/cm                                              Concave grating    13000 lines/cm                                                                 R.sub.c = 100 cm                                            Spectral range     2200-2700                                                   Spatial resolution at the                                                                         <10 μm                                                   focal plane                                                                    Entrance slit height                                                                              3.2 mm                                                      Entrance slit width                                                                               <D.sub.m /3.2                                               Magnification      3.2                                                         Linear dispersion (dλ/ds)                                                                  75 Å/cm                                                 ______________________________________                                    

The parameters of the UV Fabry-Perot filter for narrow and moderate spectral bandwidths are shown in Table V along with the experimentally demonstrated IV Fabry-Perot filter operational characteristics of interest.

                  TABLE V                                                          ______________________________________                                         UV FABRY-PEROT OPERATIONAL CHARACTERISTICS                                                        Value moderate/high                                         Characteristic     spectral resolution                                         ______________________________________                                         Finesse            37                                                          Cavity spacing     75/150 μm                                                Inter-order contrast                                                                              0.002                                                       Spectral range     2250-2650 Å                                             ______________________________________                                    

Table VI shows the Imaging Channeled Spectrograph operational characteristics as calculated from Table III and the operational parameters of the UV Fabry-Perot filter and fstW.

                  TABLE VI                                                         ______________________________________                                         IMAGING CHANNELED SPECTROGRAPH                                                 OPERATIONAL CHARACTERISTICS                                                    Characteristic      Value moderate/high                                        λ.sub.m = 2450 Å                                                                        spectral resolution                                        ______________________________________                                         Spectral resolution (FWHM)                                                                         0.11/0.05 Å                                            Spectral separation between                                                                        4.0/2.0 Å                                              channels                                                                       Linear separation between                                                                          0.053/0.027 cm                                             channels                                                                       Linear channel width at                                                                            169 μm/81 μm                                         the entrance slit                                                              Linear channel height at                                                                           3.2 mm                                                     the entrance slit                                                              Lateral chromatic aberration                                                                       4.1 μm/2.1 μm                                        at the entrance slit                                                           Spatial resolution along                                                                           4.4 μm/3.2 μm                                        the dispersion direction                                                       Spatial resolution along                                                                           0.4 sec of arc                                             the entrance slit                                                              Spectral range      2250-2650 Å                                            Total number of channels                                                                           100/200                                                    Out of band rejection                                                                              0.002                                                      ______________________________________                                    

The Imaging Channeled Spectrograph optical design achieves high spatial and spectral resolution over a large spectral range. A ray race of the preliminary optical design revealed the largest spot sizes at the focal plane to be less than 10 μin diameter. The Imaging Channeled Spectrograph spectral resolution varies directly with the Fabry-Perot filter cavity spacing. Both narrow (0.05 Å) and moderate (0.11 Å) Fabry-Perot filter spectral bandwidths are possible.

By combining Fabry-Perot filter 16 with the wide-slit imaging grating spectrograph, this invention produces a channeled spectrum consisting of a row of monochromatic images of entrance slit. Each channel corresponds to a single monochromatic image which, in turn, corresponds to a single Fabry-Perot filter transmission spike. Since the bandwidth of Fabry-Perot filter 16 determines the channel spectral bandwidth, the width of wide-slit 12 does not degrade the spectral resolution of Imaging Channeled Spectrograph 10. The width of image C is determined by the width of entrance slit 12, and the separation of images at focal plane 22 is determined by the frequency separation between spikes B. Channel/image overlap is prevented by adjusting the width of entrance slit 12, until the image width is less than the linear spacing between channels. The spectral coverage is limited only by the stopband of the coatings of Fabry-Perot filter 16, and the usable frequency range of gratings 18 and 20. Thus, a single exposure taken at focal plane 22 produces a series of high resolution, non-overlapping, two dimensional monochromatic images covering a broad spectral range.

Although the invention has been described with respect to exemplary embodiments thereof, it will be understood by those skilled in the art that variations and modifications can be effected in these exemplary embodiments without departing from the scope and spirit of the invention. 

I claim:
 1. An Imaging Channeled Spectrograph comprising:a Fabry-Perot bandpass filter means for bandpass filtering a received collimated beam of light into a filtered beam; and a wide-slit imaging spectrograph for dispersing said filtered beam; and wherein said Fabry-Perot bandpass filter means and said spectrograph cooperate to produce one image of the entrance slit of said spectrograph for each frequency band passed by said filter means.
 2. The invention of claim 1, wherein said Fabry-Perot bandpass filter means comprises at least one UV Fabry-Perot bandpass filter.
 3. The invention of claim 1, wherein said wide-slit imaging spectrograph comprises a tandem Wadsworth configuration spectrograph.
 4. An Imaging Channeled Spectrograph comprising:an entrance slit for receiving light from a source to be analyzed; a collimator means for collimating said light from said entrance slit; a Fabry-Perot bandpass filter means for filtering said collimated beam; a grating means for diffracting said filtered beam; and a spherical grating for focusing said diffracted spectrum onto a focal plane; and wherein said collimator means, said filter means, said grating means, and said spherical grating cooperate to produce a plurality of two-dimensional, monochromatic images of said entrance slit.
 5. The invention of claim 4, wherein said Fabry-Perot bandpass filter means comprises at least one UV Fabry-Perot bandpass filter.
 6. The invention of claim 4, wherein said wide-slit imaging spectrograph comprises a tandem Wadsworth configuration spectrograph. 